Many people hold this truth to be self-evident that universities should enroll more female students in science and engineering; the main question then being how. Typical arguments include possible benefits to women, possible benefits to the economy, and the unfairness of the current female under-representation. However, when clearly stated and scrutinized these arguments in fact lead to the conclusion that there should be more women in scientific disciplines in higher education in the sense that we should expect more women (which various kinds of discrimination may prevent), not that we should actively enroll more women. Outreach programs towards high school students may therefore be logically incompatible with the arguments supposed to justify them. They should purport to allow women to graduate in a field congruent with her abilities and desires, rather than try to draw as many of them to scientific disciplines as possible: one cannot try to ‘recruit’ as many female students as possible while claiming to help them choose more freely.